function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta


J = 1/m *(- y'*log(sigmoid(X*theta))-(1-y)'*log(1-sigmoid(X*theta)))+...
lambda/(2*m)*(theta(2:end)'*theta(2:end));

grad(1) = 1/m * X(:,1)'*(sigmoid(X*theta)-y);
grad(2:end) = 1/m * X(:,2:end)'*(sigmoid(X*theta)-y) + ...
    lambda/m * theta(2:end);




% =============================================================

end
